1,721,002 research outputs found
A group-theoretical version of Hilbert's theorem 90
No full textIt is shown that for a normal subgroup N of a group G, G/N cyclic, the kernel of the map Nab→> Gad satisfies the classical Hilbert 90 property (cf. Theorem A). As a consequence, if G is finitely generated, |G: N| < ∞, and all abelian groups Hab, N ⊆ H ⊆ G, are torsion free, then Na must be a pseudo-permutation module for G/N (cf. Theorem B). From Theorem A, one also deduces a non-trivial relation between the order of the transfer kernel and co-kernel which determines the Hilbert-Suzuki multiplier (cf. Theorem C). Translated into a number-theoretical setting, one obtains a strong form of Hilbert's theorem 94 (Theorem 4.1). In case that G is finitely generated and N has prime index p in G there holds a 'generalized Schreier formula' involving the torsion-free ranks of G and N and the ratio of the order of the transfer kernel and co-kernel (cf. Theorem D)
Unimodular totally disconnected locally compact groups of rational discrete cohomological dimension one
Full text linkIt is shown that a Stallings–Swan theorem holds in a totally disconnected locally compact (= t.d.l.c.) context (cf. Theorem B). More precisely, a compactly generated CO-bounded t.d.l.c. group G of rational discrete cohomological dimension less than or equal to 1 must be isomorphic to the fundamental group of a finite graph of profinite groups. This result generalises Dunwoody’s rational version of the classical Stallings–Swan theorem to t.d.l.c. groups. The proof of Theorem B is based on the fact that a compactly generated unimodular t.d.l.c. group with rational discrete cohomological dimension 1 has necessarily non-positive Euler–Poincaré characteristic (cf. Theorem H)
Rational discrete cohomology for totally disconnected locally compact groups
Full text linkRational discrete cohomology and homology for a totally disconnected locally compact group G are introduced and studied. The Hom-⊗ identity associated to the rational discrete bimodule Bi(G) allows to introduce the notion of rational duality group in analogy to the discrete case. It is shown that a semi-simple algebraic group G(K) defined over a non-discrete, non-archimedean local field K is a rational t.d.l.c. duality group, and the same is true for certain topological Kac-Moody groups. Indeed, for these groups the Tits (or Davis) realization of the associated building is a finite-dimensional model of the classifying space E_C(G(K)) one may define for any t.d.l.c. group. In contrast, Y. Neretin's group of spheromorphisms of a locally finite regular tree is not even of finite rational discrete cohomological dimension
Oriented right-angled Artin pro- groups and maximal pro- Galois groups
Full text linkFor a prime number we introduce and study oriented right-angled Artin
pro- groups (oriented pro- RAAGs for short)
associated to a finite oriented graph and a continuous group
homomorphism . We show
that an oriented pro- RAAG is a Bloch-Kato
pro- group if, and only if,
is an oriented pro- group
of elementary type generalizing a recent result of I. Snopche and P. Zalesskii.
Here
denotes the canonical -orientation on . We invest
some effort in order to show that oriented right-angled Artin pro- groups
share many properties with right-angled Artin pro--groups or even
discrete RAAG's, e.g., if is a specially oriented chordal graph, then
is coherent, generalizing a result of C. Droms. Moreover,
in this case has the
Positselski-Bogomolov property generalizing a result of H. Servatius, C. Droms
and B. Servatius for discrete RAAG's. If is a specially oriented
chordal graph and in case that
, then generalizing a well known result of M.
Salvetti.Comment: The differences between the 1st version (Apr'23) and the 2nd are:
correction of a couple of minor misprints, dedication to the memory of
Avinoam Man
Going Beyond Counting First Authors in Author Co-citation Analysis
Full text linkThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Full text link“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Full text linkWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
Dispelling the Myths Behind First-author Citation Counts
Full text linkWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
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